Project Summary Abstract Learning new tasks and exposure to new environments lead to changes in the dynamics of brain circuits, as observed in various recent experiments. The ability to embed the statistics of the environment within brain circuits is essential for animals ability to thrive and survive in changing environments. However, the mechanisms by which circuits dynamics are implemented and learned are not well understood, and pose significant theoretical challenges. Recent work in both theoretical and experimental labs has highlighted the importance of circuit dynamics. Yet in most theoretical models the network connectivity is either not plastic, or obeys biologically implausible learning rules. Here we will develop a theory of how brain circuits can learn their dynamics from the statistics of the environment. We will anchor this work in a set of experiments, in order to make it biologically realistic and limited in scope. In aim 1 we will try to understand how networks can learn stimulus-reward spatiotemporal statistics. This aim will be based on circuit level experiments that show how neuronal dynamics change due to a stimulus followed by a delayed reward, and by cellular experiments that shed light on the mechanisms of reinforcement learning. This is a problem we know more about, and it is also inherently simpler than learning the statistics of the environment in an unsupervised manner. In aim 2 we will concentrate on experiments on which cortical circuits learn the order, but not the timing, of a spatiotemporal sequence. In such networks the timing of the learned sequence are determined by intrinsic network dynamics; making this problem simpler than learning both the order and the timing of a sequence. In aim 3 we develop networks and learning rules that can learn both the order and the timing of a spatiotemporal sequence. This effort will build on results in aim 2 in which the order of events is learned in an unsupervised manner, and of aim 1 in which the timing of events is learned using reinforcement learning.